Question

Q11. What do you mean by resolution of
vectors into components? Find expressions for
components when they are inclined at right
angles to one another.

Answer 1

Resolutions of Vectors:

Resolution of vector refers to a process in which we break down a given vector into its two component smaller vectors directed along the the co-ordinate axes.

Expression for the resolved vectors:

Let us assume a vector $\vec{a}$ inclined at an angle of $\theta$ with the x axis.

In ∆ COB ;

$\therefore \: \dfrac{ \vec{a_{x}}}{ \vec{a}} = \cos( \theta)$

$\boxed{ = > \: \vec{a_{x}} = \vec{a} \cos( \theta) }$

In ∆ COD ;

$\therefore \: \dfrac{ \vec{a_{y}}}{ \vec{a}} = \sin( \theta)$

$\boxed{ = > \: \vec{a_{y}} = \vec{a} \sin( \theta) }$

Hope It Helps.

Answer 2

Answer:

Resolution of Vectors into Components

Explanation:

Resolution of vectors turns out to be meaningful, when we think resolution in terms of vectors at right angles. In that case, associated triangle is a right angle. The vector being resolved into components is represented by the hypotenuse and components are represented by two sides of the right angle triangle.

In two dimensions, a force can be resolved into two mutually perpendicular components whose vector sum is equal to the given force. The components are often taken to be parallel to the x- and y-axes. In two dimensions we use the perpendicular unit vectors i and j (and in three dimensions they are i, j and k).